ISEE top Level Quantitative help » Numbers and also Operations » determinants / Multiples » prime Numbers » how to find out if a number is prime     Explanation:

Every number except 1 has at least two factors - 1 and also itself. So us are in search of a number with no other components - that is, a prime.

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3 is a aspect of both 33 and also 39, and 5 is a factor of 35, so we can eliminate those choices. We cannot get rid of 37, since it is a prime, having actually only 1 and 37 as factors.

Which is the better quantity?

(a) The number of prime numbers in between 70 and 110

(b) The variety of prime number between 80 and also 120

Explanation:

The primes in between 80 and also 110 are contained in both sets, so all we have to do is to to compare the variety of primes between 70 and 80 and also the number of primes in between 110 and also 120.

(a) The primes in between 70 and 80 space 71, 73, and 79 - three primes

(b) The only prime between 110 and 120 is 113.

(a) is the greater quantity

Which is the higher quantity?

(a) The number of prime numbers in between 1 and 20 inclusive

(b) The variety of composite numbers between 21 and 30 inclusive

Explanation:

(a) The prime numbers in between 1 and also 20 inclusive room 2, 3, 5, 7, 11, 13, 17, 19 - eight total.

(b) The element numbers between 21 and 30 inclusive space 23 and also 29 - two prime numbers the end of ten integers. This leaves eight composite numbers.

(a) and (b) are therefore equal.

Which is the better quantity?

(a) The number of prime numbers in between 1 and 20 inclusive

(b) The number of composite numbers between 1 and 20 inclusive

Explanation:

The element numbers in between 1 and 20 inclusive are 2, 3, 5, 7, 11, 13, 17, 19 - eight total. Since 1 is neither prime no one composite, this leaves 11 composite numbers. (b) is the greater quantity.

Which is the higher quantity?

(a) The amount of the prime numbers in between 11 and 19 inclusive

(b) The amount of the composite numbers between 11 and also 19 inclusive

Explanation:

(a) The prime numbers in the 11-19 range are 11, 13, 17, and 19. Your sum: (b) The composite numbers in the 11-19 selection are 12, 14, 15, 16, and also 18. Their sum: (b) is greater.

Which quantity is greater?

(a) The number of composite numbers between 1 and 1,000 inclusive.

(b) The number of even integers between 1 and 1,000 inclusive.

Explanation:

It is not necessary to count all of the composite number in the 1-1,000 range. Other than for 2, every also number is composite, and also there are an ext than one odd composite number (15, 25) to comprise for 2. This renders (a) greater.

Which is the greater quantity?

(a) The number of primes in between 20 and also 50

(b) The variety of primes in between 10 and also 40

Explanation:

The primes in between 20 and 40 are contained in both sets, so every we have to do is to to compare the variety of primes between 40 and also 50 v the number of primes in between 10 and also 20.

(a) The primes between 40 and also 50 space 41, 43, and 47 - three.

(b) The primes between 10 and also 20 are 11, 13, 17, and also 19 - four.

Since the variety of primes between 10 and 20 outnumbers those between 40 and 50, the variety of primes between 10 and 40 outnumber those between 20 and also 50. Therefore, (b) is the greater.

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